Algebraic Geometry Seminar
Sam Grushevsky
Princeton University
Differentials with real periods and the geometry of the moduli space of curves
Abstract: Motivated by constructions in the Whitham theory (perturbation
theory for integrable systems), we consider meromorphic differentials with
prescribed singular parts and real periods on Riemann surfaces. We use these
differentials to define real-analytic foliations of $M_g$ with complex leaves,
and to give a short proof of the Diaz' bound on the dimension of complete
subvarieties of $M_g$; potential further applications will also be discussed.
No familiarity with integrable systems is assumed. Joint work with Igor
Krichever
Friday November 14, 2008 at 4:30 PM in SEO 636